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• Math textbooks
  ...960988/artofproblems-20 Statistical Theory and Bayesian Analysis] by James O. Berger.
  7 KB (901 words) - 14:11, 6 January 2022
• 1954 AHSME Problems/Problem 46
  pair O=(0,3/8); draw(Circle(O,3/16));
  3 KB (415 words) - 18:01, 24 May 2020
• 2015 IMO Problems
  ...ath>ABC</math> has circumcircle <math>\Omega</math> and circumcenter <math>O</math>. A circle <math>\Gamma</math> with center <math>A</math> intersects
  4 KB (692 words) - 22:33, 15 February 2021
• MathCounts historical results
  * 1994: William O. Engel, [[Illinois Mathcounts]]
  6 KB (565 words) - 09:40, 18 May 2023
• USAMO historical results
  **Evan O'Dorney **Evan O'Dorney
  10 KB (1,317 words) - 08:16, 23 April 2024
• Geometric mean
  ...following situation: if <math>AB</math> is a [[chord]] of [[circle]] <math>O</math> with [[midpoint]] <math>M</math> and <math>M</math> divides the [[di
  2 KB (282 words) - 22:04, 11 July 2008
• Fermat's Little Theorem
  ...mutes the necklace in a single orbit which we can denote as <math>\mathcal{O}</math> (since the size of the orbit is a factor of <math>p</math>). Hence <center><cmath>|\mathcal{O}|=\frac{1}{|G|}\sum_{g\in G}|\text{Fix}(g)|=\frac{1}{p}\sum_{g\in C_p}|\tex
  16 KB (2,675 words) - 10:57, 7 March 2024
• Cyclic quadrilateral
  * <math>\angle A + \angle C = \angle B + \angle D = {180}^{o} </math> This property is both sufficient and necessary (Sufficient & neces
  1 KB (162 words) - 20:39, 9 March 2024
• Number theory/Advanced
  ...vertically upward as the point at infinity. We denote it by <math>\mathcal{O}</math>. ...>-axis. We may thus summarize the group law by saying <math>P+Q+R=\mathcal{O}</math> if and only if <math>P,Q</math> and <math>R</math> lie on a line.
  5 KB (849 words) - 16:14, 18 May 2021
• Divisor
  ...floor\frac N2\right\rfloor+\dots+\left\lfloor\frac NN\right\rfloor= N\ln N+O(N)}</math>
  1 KB (274 words) - 19:50, 29 August 2023
• 1988 AJHSME Problems/Problem 5
  label("O",(-2.5,0),W);
  1 KB (160 words) - 16:53, 17 December 2020
• Law of Sines
  pair A=(-1,5), B=(-4,-1), C=(4,-1), D, O; O = circumcenter(A,B,C);
  4 KB (658 words) - 16:19, 28 April 2024
• Homothety
  ...ABCD</math> and <math>A'B'C'D'</math> are homothetic with respect to <math>O</math>. label("$O$",(0,0),SW);
  3 KB (532 words) - 01:11, 11 January 2021
• 2000 AMC 12 Problems/Problem 1
  ...2001 </math>. What is the largest possible value of the sum <math>I + M + O</math>? ...clear that this is true, and in this situation, the value of <math>I + M + O</math> would be <math>18</math>. Now, we use this process on <math>2001</ma
  2 KB (276 words) - 05:25, 9 December 2023
• 1985 IMO Problems/Problem 5
  A circle with center <math>O</math> passes through the vertices <math>A</math> and <math>C</math> of the Let <math>\Omega, \Omega', \omega</math> and <math>O,O',O''</math> be the circumcircles and circumcenters of <math>AKNC, ABC, BNKM,</
  3 KB (496 words) - 13:35, 18 January 2023
• Trigonometry
  ...'''C'''osine = '''A'''djacent / '''H'''ypotenuse, and '''T'''angent = '''O'''pposite / '''A'''djacent
  8 KB (1,217 words) - 20:15, 7 September 2023
• Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality
  pair O=(0,0),A=(-1,0),B=(0,1),C=(1,0),P=(1/2,0),Q=(1/2,sqrt(3)/2),R=foot(P,Q,O); draw(B--O--C--arc(O,C,A)--O--R--P); rightanglemark(O,P,R);
  5 KB (912 words) - 20:06, 14 March 2023
• Riemann Hypothesis
  ...nt statement of the Riemann hypothesis is that <math>\pi(x)=\mathrm{Li}(x)+O(x^{1/2}\ln(x))</math>.
  2 KB (425 words) - 12:01, 20 October 2016
• Power of a Point Theorem
  Consider a circle <math>O</math> and a point <math>P</math> in the plane where <math>P</math> is not
  5 KB (827 words) - 17:30, 21 February 2024
• Algebraic geometry
  ...topological space isomorphic to some <math>(\operatorname{Spec }A,\mathcal{O}_{\operatorname{Spec}A})</math>. ...ting an open covering <math>\{U_i\}_i</math> such that <math>(U_i,\mathcal{O}_{X|U_i})</math> is an affine scheme for every <math>i</math>.
  2 KB (361 words) - 01:59, 24 January 2020

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